Séminaire d'analyse

Pour toute question relative à l'organisation, merci de contacter Cristina Benea, Joackim Bernier ou Joe Viola.

Ramona Haeberli
Etablissement de l'orateur
Université de Genève
Date et heure de l'exposé
Lieu de l'exposé
salle Eole
Résumé de l'exposé

Splitting schemes are a natural and easy to implement approach to integrate numerically in time differential equations. However, high order splitting methods suffer in general from an order reduction phenomena when applied to the integration of partial differential equations with non-periodic boundary conditions. In this talk, inspired by recent corrector techniques for the second order Strang splitting method, we present a new splitting method of order three for a class of semilinear parabolic problems that avoids order reduction. We prove the third order convergence of the method in a simplified linear setting and confirm the result by numerical experiments. Moreover, we observe numerically that the high order convergence persists for an order four variant of a splitting method, and also for a nonlinear source term.

Frédéric Marbach
Etablissement de l'orateur
ENS Paris
Date et heure de l'exposé
Lieu de l'exposé
salle Eole
Résumé de l'exposé

In this presentation, we will construct regular solutions to linear and nonlinear elliptic-parabolic equations in which the natural direction of parabolicity reverses along a critical line. To prevent the emergence of singularities, we will impose orthogonality conditions on the source terms, and follow them during the execution of the nonlinear schemes.

This is a joint work with Anne-Laure Dalibard and Jean Rax, motivated by recirculation problems in boundary layer theory for fluid mechanics, and based on the preprint https://arxiv.org/abs/2203.11067

Angeliki Menegaki
Etablissement de l'orateur
Imperial College London
Date et heure de l'exposé
Lieu de l'exposé
Salle Eole
Résumé de l'exposé
Denis Grebenkov
Etablissement de l'orateur
Ecole Polytechnique, CNRS
Date et heure de l'exposé
Lieu de l'exposé
Résumé de l'exposé